Question

9 lines l,m,n, and j are shown in the xy - coordinate plane. determine which line matches each equation.
(1) y=-1 + x
(2) y=-4-\frac{1}{3}x
(3) y = 2-3x
(4) y=2-\frac{1}{2}x

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Analyze equation (1) $y=-1 + x$

Here, $m = 1$ (positive slope) and $b=-1$. A line with a positive slope rises from left to right and has a y - intercept of - 1.

Step3: Analyze equation (2) $y=-4-\frac{1}{3}x$

The slope $m=-\frac{1}{3}$ (negative slope) and $y$ - intercept $b = - 4$. A line with a negative slope falls from left to right and crosses the y - axis at - 4.

Step4: Analyze equation (3) $y = 2-3x$

The slope $m=-3$ (negative slope) and $y$ - intercept $b = 2$. The line has a steeper negative slope compared to the others with negative slopes and crosses the y - axis at 2.

Step5: Analyze equation (4) $y=2-\frac{1}{2}x$

The slope $m =-\frac{1}{2}$ (negative slope) and $y$ - intercept $b = 2$. It has a less steep negative slope compared to the line in equation (3) and crosses the y - axis at 2.

Answer:

Without the actual names of the lines in the graph, we can only describe the characteristics:
(1) Positive - slope line with y - intercept of - 1.
(2) Negative - slope line with y - intercept of - 4.
(3) Steep negative - slope line with y - intercept of 2.
(4) Less steep negative - slope line with y - intercept of 2.